We initialized the system with a solute/solvent ratio \(c_s^B/c_f^B=1\)  and an average solution density in the box of \(\bar{c}=0.75 \sigma _0^{-3}\) .
We swapped particle identity in the reservoirs every 20 time steps, with a time step of \(\Delta t = 0.05\tau \) .
We let the system equilibrate for \(10^7\)  steps.
By doing this, we achieve both equilibration of solutes around the colloid and the desired concentration gradient between the control volumes.
The equations of motion were integrated using a velocity-Verlet algorithm, and we kept the temperature of the system at \(k_BT/\epsilon _0=1.0\)  using a Nosé-Hoover thermostat [1]}.
After equilibration, we ran \(10^7\)  production steps to sample the flow profile around the colloid and the concentration distribution for each species.
